(d) | Ta2 – 4)3 dx -

Q: Show that 2x° dx = [; 2r° dx + f zr* dx + [,2x° dx %3D

A: Given that,    ∫142x2dx=∫122x2dx+∫232x2dx+∫342x2dx

Q: use a geometry formula to find the exact value of the definite integral (x/2 +3)dx on interval[-2,4]

A: To calcute the value of the definite integral ,using geometric consideration (ie. without using…

Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A: Integration by parts:∫uvdx = 4∫vdx - ∫[ddx(u)∫ vdx]dx

Q: -0.5 3. f5 x(1-x)³ dx 0

A: To evaluate the given definite integral by using substitution rule.∫00.5x1-x3 dx

Q: Evaluate the integral in terms of Beta function: ∫x^12(1−x)^16 dx    limit: 0 to 1

A:

Q: Evaluate the integral.  integral  sec 2 x  tan  3 x  dx

A: Consider the following integral:

Q: What is the integral of x2(2-x)^(1/3) dx on the interval [1,2]?

A:

Q: 56. 1 dx V1+9x2

A: Given, ∫dx1+9x2

Q: 8. Evaluate x dx from the definition of RS-integral.

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) x' dx

A:

Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) tan-(5x) dx 1 + 25x2 1 2…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 4 tan(x) sec (x) dx

A: Given the integral, ∫4tan(x)sec3(x) dx = I(Say) Now, I=∫4tan(x)Sec(x)sec2(x) dx.........(1)  Now…

Q: Evaluate the definiteIntegral. integral 1/2 to 1 cosx^-2/x^3 dx

A: The given integral is ∫121cosx-2x3dx. Let u=x-2. Then, du=-2x-3. The lower limit will become…

Q: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (tan²(x) tan^(x) dx

A: Given       I=∫7tan2x++tan4xdx      = 7∫tan2x1+tan2xdx      = 7∫tan2x.sec2x dx∵sec2x-tan2x=1

Q: (c) dx 1 – x2 (d) | Va? + x² dx

A:

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 9x…

A:

Q: Compute this improper integral showing all steps.  integral of x ln(x) dx from 0 to 2.

A:

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

A:

Q: Find the indefinite integral using integration by parts wi X Cos 6x dx;u = x, dv = cos 6x dx %3D

A:

Q: Evaluate the indefinite integral using integration by parts $3xe2=dx re - e +C ze +e +C ze +C 6xe2 -…

A:

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: 1. Evaluate the integral using integration by parts where possible. Z2 x In(8x)dx

A: we  have ∫12x*ln(8x) dx   we have to apply integration by parts ∫u v dx = u∫v dx −∫u' (∫v dx) dx…

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 7x…

A:

Q: (e) / V1 + x² dx (f) x² + 4 dx

A:

Q: Using only the definition of RS-integral, evaluate |x* d[x}.

A:

Q: 5+ 2x dx x(3x² – 4)5 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) sec (x) dx

A:

Q: Evaluate the integral by u-substitution. (Use C for the constant of integration.) Integral of…

A: Given : Integral ∫Sin3(x) cos(x) dx   To find : Evaluate the integral by u-substitution?

Q: Evaluate x dx from the definition of RS-integral.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integra 9 dx 8V1- x2

A:

Q: (e) / 3. (c) (Зх — 5)3 dx (d) / ((V– 5)² – x)² c - -

A: (c)

Q: Use integration by parts to evaluate the definite integral. | t² In(t)dt Give an exact answer

A:

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: (a) /(3=² (За? — 6х + 5) dx - 1 .5 x° + 5 1 (b) dx - 4

A: To determine the value of definite integrals.

Q: Evaluate the folowing indefinite integral. 1 dx 5 2x dx = 2x = xp (Use C as the arbitrary constant.)

A:

Q: -1Vx X. dx Vx cos

A:

Q: intergrate the integral from 0 to 1 of (x^2 + x + 1)/((x+1)^2)(x+2)) dx

A: See the details solution in below

Q: Find the general indefinite integral. (Use C for the constant of integration.)

A:

Q: a) Evaluate the indefinite integrals using Tabular Integration by parts. i) S(x² +x + 1)Sinxdx

A: Given: The integral  ∫(x2+x+1) sin(x) dx

Q: Using only the definition of RS-integral, evaluate x* d[x].

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 5 tan(x)sec^3(x)dx

A:

Q: Evaluate the indefinite integral using u substitution  x^6sin(x^7) dx

A:

Q: dx V1-x -1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | tan (x) sec(x) dx

A: Consider the integral ∫tan3xsecxdx

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. X Cos 8x…

A:

Q: Use integration by parts to evaluate the definite integral. 4t2 In(t)dt

A: We have to evaluate ∫1e4t2 ln(t) dt  by using integration by parts.

Q: Use residues to find the indefinite integral f* dx- (16+x)2 2x2

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.